Find the route of following quadratic …
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Sia ? 6 years, 6 months ago
we have, 2x2 + x - 4 = 0
Dividing both sides by 2, we have
{tex}x^2 +{1 \over 2}x - 2 =0{/tex}
{tex}\implies x^2 + {1\over2} x +{1 \over 16} = 2 + {1 \over 16}{/tex}
{tex}\implies (x)^2 + 2 (x) {1 \over 4} + ({1 \over 4})^2 = {32+1 \over16}{/tex}
{tex}\implies (x + {1 \over 4})^2 = {33 \over 16}{/tex}
{tex}\implies (x + {1 \over 4}) = \pm {\sqrt 33 \over 4}{/tex}
{tex}\implies x = {\sqrt33 \over 4} - {1 \over4}, \, -{\sqrt33 \over 4} - {1 \over4}{/tex}
{tex}\implies x = {\sqrt 33 - 1 \over 4},\, {-\sqrt33 - 1 \over 4}{/tex}
{tex}\therefore x = {\sqrt 33 - 1 \over 4},\, {-\sqrt33 - 1 \over 4}{/tex} are the required roots.
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